As far as the RN is concerned, the custom has become established that a surface unit designed around a primary asw role is designated as a frigate, whereas a surface unit designed primarily around anti-air is designated as a destroyer. In this system size is not a determining factor, as some frigates where larger than destroyers. Of course, a lot of 'fudging' goes on, such as when the RN categorised the Invincible as a 'through deck cruiser', to baffle the brains of the politicians (a long story, but more or less the RAF always seeing its role to 'sink' any British aircraft carrier) Bearing this in mind, it might be wise for the Navy to re-classify the new carriers as auxiliaries' to keep them hidden
Re the Ikara, I'm not sure if what you've got would be enough. Like the Seaslug, it was assembled prior to launch, so needed some space for storage and handling. I'm not an expert, but it looks as though the RAN and RN used diferent systems, the former seeming to be more compact, while the latter used a 'gazebo' style of launching that was sited forward, as with the Bristol and the rebulit Leander's. By all accounts it seems the RN system was very noisy, not a good thing when hunting subs.